# omni.ate: Omnibus function for estimation and testing In ri: ri: R package for performing randomization-based inference for experiments

## Description

Estimates the average treatment effect (ATE) and inferential statistics under constant effects hypotheses. Estimation is without covariate adjustment, via weighted least squares.

## Usage

 `1` ```omni.ate(Y, Z, perms, invert = FALSE, quantiles = c(0.025, 0.975)) ```

## Arguments

 `Y` numeric vector of length N, outcome variable `Z` binary vector (0 or 1) of length N, treatment indicator `perms` N-by-r permutation matrix, as output by `genperms` or `genperms.custom` `invert` logical for generating constant effects confidence intervals through exact test inversion, with the difference-in-means as a test statistic. Default is `FALSE`. `quantiles` vector of quantiles of the randomization distribution to be returned. Quantiles also used to determine endpoints of confidence intervals. Default is equal-tailed 95% intervals.

## Details

`omni.ate()` is a convenience function that implements a number of functions otherwise available in `ri`. Greater flexibility through use of the individual functions involved.

## Value

 `ate` estimated average treatment effect `greater.p.value` one-tailed p-value: proportion of randomizations yielding estimated ATE greater than or equal to hypothesized ATE `lesser.p.value` one-tailed p-value: proportion of randomizations yielding estimated ATE less than or equal to hypothesized ATE `p.value` two-tailed p-value: twice the smaller of the two one-tailed p-values, as advocated by Rosenbaum (2002) `p.value.alt` two-tailed p-value: proportion of randomizations yielding absolute estimated ATE greater than or equal to absolute hypothesized ATE `se.null` standard error of the randomization distribution assuming a zero treatment effect `conf.int` confidence interval approximation under a constant effect hypothesis `se` standard error of the randomization distribution assuming a constant treatment effect equal to the estimated ATE `conf.intInv` (Optional, if `invert=TRUE`) confidence interval under an inverted exact test with the difference-in-means as a test statistic

## Author(s)

Peter M. Aronow <[email protected]>; Cyrus Samii <[email protected]>

## References

Gerber, Alan S. and Donald P. Green. 2012. Field Experiments: Design, Analysis, and Interpretation. New York: W.W. Norton.

Rosenbaum, Paul R. 2002. Observational Studies. 2nd ed. New York: Springer.

Samii, Cyrus and Peter M. Aronow. 2012. On Equivalencies Between Design-Based and Regression-Based Variance Estimators for Randomized Experiments. Statistics and Probability Letters. 82(2): 365-370. http://dx.doi.org/10.1016/j.spl.2011.10.024

`ri`
 ```1 2 3 4 5 6 7``` ```y <- c(8,6,2,0,3,1,1,1,2,2,0,1,0,2,2) Z <- c(1,1,0,0,1,1,0,0,1,1,1,1,0,0,1) perms <- genperms(Z) # all possible permutations of assignment omni.ate(y,Z,perms,FALSE) # omni.ate(y,Z,perms,TRUE) # may take some time to run ```